Dynamic Algorithms for Online Multiple Testing

We demonstrate new algorithms for online multiple testing that provably control false discovery exceedance (FDX) while achieving orders of magnitude more power than previous methods. This statistical advance is enabled by the development of new algorithmic ideas: earlier algorithms are more "static" while our new ones allow for the dynamical adjustment of testing levels based on the amount of wealth the algorithm has accumulated. We also prove relationships between controlling FDR, FDX, and other error metrics for our new algorithm, SupLORD, and how controlling one metric can simultaneously control all error metrics. We demonstrate that our algorithms achieve higher power in a variety of synthetic experiments.